Suppressing self-excited vibrations of mechanical systems by impulsive force excitation
|
|
- Louise Pitts
- 6 years ago
- Views:
Transcription
1 Journal of Physics: Conference Series PAPER OPEN ACCESS Suppressing self-excited vibrations of mechanical systems by impulsive force excitation To cite this article: Thomas Pumhössel 26 J. Phys.: Conf. Ser View the article online for updates and enhancements. Related content - Study on hydraulic exciting vibration due to flexible valve in pump system with method of characteristics in the time domain Y H Yu, D Liu, X F Yang et al. - Self-Excited Potential Oscillation of Lipid across a Micropore Controlled by Hydrostatic Pressure Seimei Sha, Takamichi Nakamoto and Toyosaka Moriizumi - Airflow energy harvesters of metal-based PZT thin films by self-excited vibration E Suwa, Y Tsujiura, F Kurokawa et al. This content was downloaded from IP address on 5/2/28 at :5
2 MOVIC26 & RASD26 Journal of Physics: Conference Series 744 (26) 2 doi:.88/ /744//2 Suppressing self-excited vibrations of mechanical systems by impulsive force excitation Thomas Pumhössel Institute of Mechatronic Design and Production, Johannes Kepler University Linz, Austria thomas.pumhoessel@jku.at Abstract. In this contribution, self-excited mechanical systems subjected to force excitation of impulsive type are investigated. It is shown that applying force impulses which are equally spaced in time, but whose impulsive strength depends in a certain manner on the state-variables of the mechanical system, results in a periodic energy exchange between lower and higher modes of vibration. Moreover, in the theoretical case of Dirac delta impulses, it is possible that no energy crosses the system boundary while energy is transferred across modes, i.e. neither external energy is fed to the mechanical system, nor energy is extracted from the mechanical system. Shifting energy to higher modes of vibration, whose natural damping is larger compared to lower ones, results in a faster dissipation of energy. An analytical stability investigation is presented using the assumption of impulsive forcing of Dirac delta type, which allows deciding easily about the stability by evaluating the eigenvalues of the coefficient matrix of a corresponding set of difference equations. It is shown that the developed impulsive forcing concept is capable to suppress self-excited vibrations of mechanical systems. Some numerical results of a simple mechanical system with two degrees of freedom underline the presented approach.. Introduction Since a long time, self-excited vibrations of mechanical systems are, due to their dangerous nature, of interest to the engineering community. Hence, a lot of measures have been developed to avoid them. Their characteristic of feeding external energy to a mechanical system naturally leads to the question if this energy can be redirected in a way to finally achieve a stable system. One possibility is the introduction of nonlinear energy sinks (NES), see [], for example. NES were first introduced for reducing vibrations of mechanical systems with initial excitation, see [2] for a variety of detailed investigations. It was shown that lightweight NES which are passively coupled to a primary mechanical structure allow to efficiently transfer vibration energy from the primary system to the NES in an unidirectional manner. Within the NES, the vibration energy is dissipated, and hence, a reduction of vibrations of the primary structure is achieved. An other mechanism using nonlinear energy sinks is investigated in [3]. Therein, vibro-impact NES are introduced to transfer energy across modes of vibration. On a primary structure, two additional moveable masses are installed, which may exhibit impacts with the primary structure. It is demonstrated, that these impacts can lead to a modal redistribution of energy in the sense, that energy is transferred from lower to higher modes, resulting in a faster decrease of vibrations. The modal transfer of energy in systems with a periodically and continuously varying stiffness parameter was investigated in [4] and [5], for example. At certain frequencies of the varying Content from this work may be used under the terms of the Creative Commons Attribution 3. licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by Ltd
3 MOVIC26 & RASD26 Journal of Physics: Conference Series 744 (26) 2 doi:.88/ /744//2 stiffness parameter, which where reported in [6], a periodic and bidirectional modal transfer of energy can be observed. By contrast to NES-systems, which are of passive nature, external energy is necessary in this case. In [7], the effect of switching a stiffness between two predefined levels is studied. It is shown that a transfer of energy from low modes of one stiffness state, to high modes of the other stiffness state is possible. Unidirectional modal energy transfers applying stiffness impulses were investigated in [8], and the capabilities of suppressing self-excited vibrations were demonstrated in [9]. A correct timing of theapplication of theimpulses is necessary in both cases toensureenergy transfers inonly one direction, i.e. from low to high modes, and in general, the applied impulses are not equidistant in time. In this contribution, a method using impulsive forcing is proposed to rearrange the modal energy distribution of self-excited dynamical systems in a way which allows to stabilize the otherwise unstable system. Therefore, impulsive forces, which are equidistant in time, but whose strength is state-dependent, are introduced. It is shown, that a transfer of discrete amounts of energy across modes of vibrations is possible, where the direction of transfer depends on the state of the system at the instant of time the impulse is applied. Moreover, it is demonstrated that certain states of the mechanical system exist where, in the theoretical case of Dirac delta force impulses, neither energy is fed to the mechanical system, nor energy is extracted from it. The repeated application of such impulses according to the proposed approach results in a description of the system dynamics at discrete, equidistant instants of time by a set of difference equations. Therewith, the stability of the trivial solution can be investigated by calculating the eigenvalues of the corresponding coefficient matrix. Numerical stability investigations of a mechanical system with two degrees of freedom show that the proposed method allows to suppress self-excited vibrations. 2. Analytical investigations Assume that the equations of motion of a n-dimensional mechanical system are given in the following form K Mx +Cx +Kx = ε k δ(τ τ k )f, () where x represents the displacement vector, ( ) denotes differentiation with respect to, andmand K arethe constant andsymmetric mass and stiffness matrices. Itis furtherassumed, that the matrix C can be decomposed in a damping and a self-excitation part according to k= C = C d +C se, (2) hence, self-excitation mechanisms which can be modelled by negative damping coefficients are investigated in this contribution. Moreover, the mechanical system is subjected to a sequence of K force impulses of Dirac delta type applied at instants of k, see right side of Eq. (), where δ(τ τ k ) represents the Dirac delta function. Each Dirac delta impulse can be seen as the simplest approximation of e.g. a half-sine shaped impulse. The constant vector f = [f,f 2,...f n ] T (3) specifies which masses are subjected to force impulses. Introducing the scaling factor ε k allows the impulsive strength to be different for each impulse. 2
4 MOVIC26 & RASD26 Journal of Physics: Conference Series 744 (26) 2 doi:.88/ /744//2 2.. Energy transfer The effect of a single Dirac delta force impulse to the displacements and velocities of the mechanical system is investigated following []. Therefore, Eq. () is rewritten for a single impulse applied at an instant of k. Mx +Cx +Kx = ε k δ(τ τ k )f (4) The impulse on the right hand side of the above equation must be balanced with an impulse on theleft handside. If, for example, x would beof impulsive type, x would contain thederivative of the Dirac delta function, which would have to be balanced on the right hand side. Since no such function appears on the right hand side, x is not of impulsive type. Similar considerations hold for x. Hence, the only possibility is that x is an impulsive function, and therefore, x and x remain bounded at τ k. Integrating Eq. (4) over an infinitesimally small interval from τ k to τ k+, where the /+ sign denotes the instants of time just before/after application of the impulse, leads to and finally and M τk+ τ k x dτ }{{} x (τ k+ ) x (τ k ) τk+ τk+ +C x dτ +K τ } k {{} = τ k xdτ }{{} = = f τk+ δ(τ τ k )dτ ε k, (5) τ } k {{} = x (τ k+ ) = M fε k +x (τ k ), (6) x(τ k+ ) = x(τ k ). (7) A force impulse of Dirac delta type has no effect on the displacements x, see Eq. (7), i.e. the potential energy of the mechanical system remains constant across an impulse, whereas the velocities x, in general, are subject of variation (6). The corresponding variation of the kinetic energy T of the overall system is given by T k = T(τ k+ ) T(τ k ), (8) where T(τ k+ ) and T(τ k ) denote the kinetic energy just after/before application of the impulse. Using Eq. (6), T k can be written in the following form T k = 2 ( f T M fε 2 k +2fT x (τ k )ε k ). (9) Obviously, T k is a quadratic function of the strength scaling factor ε k, and depends on the velocities x (τ k ) just before the impulse. Assuming that the coefficients of ε k and ε 2 k in Eq. (9) are unequal zero, the equation T k = () is fulfilled, of course, in the trivial case ε k = ε k,z =, () and in the case 2 ε k = ε k,z2 = f T M f ft x (τ k ). (2) Interestingly, in the latter case, the impulse does not have any effect on the overall energy content of the mechanical system, although the impulsive strength ε k = ε k,z2. For this reason, this 3
5 MOVIC26 & RASD26 Journal of Physics: Conference Series 744 (26) 2 doi:.88/ /744//2 case is investigated in the following in more detail. Assume that an impulse with ε k = ε k,z2 is applied to only one vibrating mass of the n-dimensional mechanical system, i.e. for the vector f in Eq. (6), f i for i = p, and f i = for i p, i,p [,n] holds. It can easily be seen, that in this case, the velocity of the respective mass M p changes its sign, but preserves its absolute value to fulfill Eq. (), i.e. the kinetic energy of the mass M p remains unchanged. Nevertheless, considering modal coordinates, the kinetic energy of each mode will, in general, be subject of variation. Therefore, a conventional modal transformation according to x = Φy (3) is introduced, where Φ comprises the eigenvectors of the corresponding undamped system of Eq. () without external forcing. Equations (6) and (7) can now be written in the form and y (τ k+ ) = Φ M fε k +y (τ k ), (4) y(τ k+ ) = y(τ k ). (5) In general, the vector Φ M f in Eq. (4) is fully occupied even if only one mass is subjected to force impulses, contrary to the vector M f in Eq. (6) which possesses elements unequal zero only at the positions corresponding to the respective masses. Hence, applying impulses only to one mass, allows to affect all modes of vibration y i, i =,...n of the mechanical system. Splitting T k in Eq. () in the modal components leads to T k = n i= T (i) k =, (6) which is fulfilled for ε k = ε k,z2 as shown earlier. Therein, the superscript (i) denotes the i-th mode of vibration. The variations T (i) k in Eq. (6) can be further grouped in modes which receive energy, and in modes from whom energy is extracted. Denoting the grouped modes as set A and set B, Eq. (6) reads T k = T A,k + T B,k =. (7) This means that energy is transferred from mode-set A to mode-set B or vice versa. It has to be pointed out, that Eq. () as well as (7) mean that no energy crosses the system boundary while energy is transferred, as the work of the impulsive forces is equal to the variation of the kinetic energy of the overall system, which is zero. Consequently, neither external energy is needed to initiate the transfer, nor is the transfer accompanied by extracting energy from the mechanical system. It is evident, that this only holds in the theoretical case of force-impulses of Dirac delta type. At that point, the question about the benefit of transferring kinetic energy across modes of vibration arises. One possible advantage comes clear if the fact that higher modes possess larger damping ratios than lower ones is taken into consideration. Hence, shifting energy from a lower, less damped mode, to a higher mode with larger damping results in a faster dissipation of the transferred energy than in the lower mode. In the case where no self-excitation is present, a faster decay of free vibrations of the mechanical system is expected. In the self-excited case, a repeated energy transfer across modes, initiated by a sequence of impulses is maybe capable to suppress the self-excited vibrations, i.e. naturally leads to the question about the stability of the mechanical system. 4
6 MOVIC26 & RASD26 Journal of Physics: Conference Series 744 (26) 2 doi:.88/ /744// Stability To investigate the stability of the trivial solution of the mechanical system, the equations of motion () are written in first order form according to with [ A = q = Aq+ K ε k δ(τ τ k )b (8) k= I M K M C ] [, and b = M f ], (9) where I represents the identity matrix. Between adjacent impulses, the mechanical system Eq. (8) has the well-known solution q(τ) = e A(τ τ k) q(τ k+ ) for τ k < τ τ k+, (2) see[], for example. The equidistance of the impulses allows to regard the timeline as a sequence of timespans τ, where the mechanical system is of autonomous type, followed by an impulse. With the abbreviation D = e A τ, and Eqs. (6) and (7), the relation between the state-vector q(τ k+ ) at the beginning τ k+ of an autonomous timespan, to the state-vector q(τ k+,+ ) just after the following impulse is of the form q(τ k+,+ ) = q(τ k+, )+ε k+ b = Dq(τ k+ )+ε k+ b. (2) Choosing ε k to be state-dependent according to Eq. (2) leads to q(τ k+,+ ) = Rq(τ k+ ), (22) which is a set of linear difference equations with constant coefficients. The coefficient matrix reads [ ] I R = D (23) I 2G with G = f T M f M f f T. (24) Equation (22) relates the state-vector at an instant of k+ to the state at τ k+,+, where τ k+,+ τ k+ = τ holds, i.e. R describes the growth of the state-vector q. Following [], R is denoted as the growth matrix of the system. Now, we can introduce a function χ(τ), similarly to [], comprising the values of the state-vector q(τ) at the instants of time,τ +,τ 2+,...τ k+,..., where with Eq. (22), χ(τ k+,+ ) = Rχ(τ k+ ) (25) holds. The question about the stability of the trivial solution of the mechanical system Eq. () with ε k according to Eq. (2) can be investigated by observing the evolution of the state-vectors in χ, which is described by the eigenvalues of the matrix R. Hence, the mechanical system Eqs. () and (2), is asymptotically stable if, and only if, for the absolute value of all eigenvalues λ i, i [,n] of R λ i < (26) holds, and unstable if the absolute value of at least one eigenvalue of R is larger than one. Deciding about the stability can either be done by numerically calculating the eigenvalues of R, or analytically by using the Schur-Cohn criterium, see [2], for example. 5
7 MOVIC26 & RASD26 Journal of Physics: Conference Series 744 (26) 2 doi:.88/ /744//2 3. Numerical example Figure () shows a sketch of the investigated mechanical model. The lateral flow with constant k k 2 U F,k m m 2 c x c 2 x 2 Figure. Investigated self-excited mechanical system with impulsive forcing of mass m. velocity U results in an axial force F s on mass m 2 in the direction of x 2. Using a linearized Rayleigh model, F s can be written in the form F s = (a bu 2 )ẋ 2. (27) Denoting c s = a bu 2, self-excitation takes place if c s < holds. The mass m is subjected to a sequence of Dirac delta force impulses F,k = ε k δ(τ τ k )f (28) where k =,2,..., and f was set to f =. Applying a time transformation τ = Ω R t, where Ω R = k R /m R represents a reference angular velocity, and introducing the non-dimensional system parameters according to M i = m i m R, K i,i = k i,i k R, C i,i = αk i,i, C s = c sω R k R, (29) i =,2, the equations of motion are of the form of Eq. (). The following non-dimensional system parameters M = M 2 =, K = K 2 =, α =., C s =.2 (3) are used for the numerical investigations. Calculating the eigenvalues of the corresponding system matrix A leads to Λ,2 =.3±.679i, and Λ 3,4 =.53±.68i, (3) just to show that C s is tuned in a way that the mechanical system without impulsive excitation is unstable. The eigenvalues λ i of the matrix R, according to Eq. (23), decide about the stability of the system with impulsive force excitation, as described in section 2.2. Obviously, they depend on the constant time τ between impulses, i.e. λ i = λ i ( τ), as the matrix D in Eq. (23) is a function of τ. Hence, the effect of τ on the stability of the trivial solution is investigated in the following. The maximum absolute value of the eigenvalues λ i for different values of τ is depicted in Fig. 2. For most values of τ, the impulsive force excitation has no stabilizing effect, as max λ i > holds. Interestingly, two small intervals with the center at about τ p and τ p2 are observed where max λ i <, i.e. the originally unstable system becomes asymptotically stable by impulsive forcing. To give insight into the physical mechanism behind, it turned out, 6
8 MOVIC26 & RASD26 Journal of Physics: Conference Series 744 (26) 2 doi:.88/ /744//2.4 max(abs(λ i )).2 stability threshold τ p τ p τ Figure 2. Maximum absolute value of the eigenvalues λ i of the matrix R for different values of the constant time τ between impulses ǫ k -.2 E y E y 2 E +E Figure 3. Timeseries of the strength scaling factor ε k, the modal coordinates y and y 2, and the modal energies E and E 2 for τ = τ p of the mechanical system without natural damping and turned off self-excitation. Initial condition: first mode deflection. that it is useful to look at the behaviour of the system when neglecting natural damping as well as switching off the self-excitation mechanism, i.e. in the equations of motion α = and C s =. Figure3showsthe correspondingtimeseries of the strengthscaling factor ε k, themodal coordinates y and y 2, and the modal energies E and E 2 for τ = τ p. As initial condition, a first mode deflection according to y (τ = ) = and y 2 (τ = ) =, (y i (τ = ) =, i =,2) is used, i.e. initially, only the first mode contains energy. At τ = τ p, the first impulse is applied with a strength according to Eq. (2). Now, the second mode contains a part of the energy of the first mode. Until the second impulse is applied, the energy content of both modes remains constant, as there is no natural damping present, and the self-excitation mechanism is turned 7
9 MOVIC26 & RASD26 Journal of Physics: Conference Series 744 (26) 2 doi:.88/ /744//2.2 ǫ k.5 E..2 y E y 2 E +E Figure 4. Timeseries of the strength scaling factor ε k, the modal coordinates y and y 2, and the modal energies E and E 2 for τ = τ p2 of the mechanical system without natural damping and turned off self-excitation. Initial condition: first mode deflection. off. In the following, a quasi-periodic sequence of impulses with strength ε k is observed, see Fig. 3 (left column, top), which is not symmetric with respect to the time-axis. This sequence of impulses results in a periodic decrease and increase of first mode vibrations y (τ), see Fig. 3 (left column, center) and an opposed modulation of second mode vibrations y 2 (τ), see Fig. 3 (left column, bottom). This means, that vibration energy is transferred between modes one and two in a periodic manner. The modal exchange of energy is shown clearly if the total modal energy contents E i, i =,2, comprising potential and kinetic energy are introduced. Figure 3(right) shows the corresponding results. At the initial =, E () and E 2 () =. With ongoing time, E decreases, as more and more energy is shifted to the second mode, resulting in an increase of E 2. At about τ 5 time-units, E has approached a minimum value (approximately 6.7% of the initial energy), and E 2 a maximum one. Thereafter, E and E 2 increase and decrease periodically, but in the opposite direction. It has to be pointed out that the impulsive forces, per definition according to Eqs. () and (2), neither add energy to, nor extract energy from the mechanical system. For this reason, the total energy content E + E 2 of the mechanical system remains constant throughout all the time, see Fig. 3 (right column, bottom). If the timespan τ between the impulses is set to τ = τ p2, the results depicted in Fig. 4 are obtained. First of all, one recognizes that ε k takes only positive values, contrary to Fig. 3. Moreover, a faster exchange of energy between the modes of vibration is observed. In principle, the same behavior as in Fig. 3 occurs, namely a periodic modal exchange of energy where the total energy content of the mechanical system remains constant. For this reason, only the case τ = τ p is investigated in the following. To further demonstrate how transferring energy across modes is capable to stabilize unstable, self-excited systems, natural damping is introduced, i.e. α =. according to Eqs. (3). 8
10 MOVIC26 & RASD26 Journal of Physics: Conference Series 744 (26) 2 doi:.88/ /744// E, E 2, E tot..5 E tot E E tot of autonomous system E 2 x ǫ k x Figure 5. Timeseries of the mechanical system with natural damping but in the absence of self-excitation. Modal energy contents E (solid) and E 2 (dotted), total energy content E tot = E +E 2, impulsive strength scaling factor ε k (left), and physical displacements x and x 2 (right) for τ = τ p. Grey-colored lines denote results of the corresponding system without impulsive excitation. Initial condition: first mode deflection. The self-excitation mechanism is still turned off, and a first mode deflection is used as initial condition. Figure 5 (left) shows the modal energy contents E and E 2, and the total energy content E tot = E +E 2. As before, a modal exchange of energy between first and second mode is observed, resulting now in a much faster decrease of E tot compared to the autonomous system (see grey colored line). In the presence of natural damping, shifting energy to the higher mode allows to utilize the enhanced damping properties of the higher mode compared to the lower one in a better way. A discrete amount of energy, which is transferred to a higher mode is dissipated in a shorter period of time in the higher mode than in the lower one. Consequently, the total energy content of the mechanical system decreases faster than in the case where no impulsive excitation is active (see grey-colored line). Figure 5 (right) shows the corresponding physical displacements x and x 2. According to the enhanced dissipation of energy, x and x 2 decrease much faster compared to the system without impulsive excitation (grey colored lines). Hence, shifting energy to higher modes using the proposed approach can also be seen as a method of active vibration suppression of mechanical systems. Henceforth, the self-excitation mechanism is turned on. According to the eigenvalues Eq. (3), the trivial solution of the autonomous system is unstable. As shown in Fig. 2, impulsive excitation with τ = τ p allows to stabilize the unstable system. Figure 6 shows the corresponding results in the time domain, where as initial condition an initial velocity of mass #2 according to x (τ = ) = and x 2 (τ = ) =, (x i(τ = ) =, i =,2) is used. As previously, the impulsive force excitation causes a repeated transfer of energy between first and second mode in both directions, but with higher frequency. Due to the enhanced utilization of the damping properties of the mechanical system, the total energy content E tot decreases to zero. In the case without impulsive excitation, E tot increases beyond all limits (see grey-colored line). The same applies for the physical displacements x and x 2, see Fig. 6 (right). 9
11 MOVIC26 & RASD26 Journal of Physics: Conference Series 744 (26) 2 doi:.88/ /744// E tot of autonomous system E, E 2, E tot.4 E tot E E 2 x ǫ k x Figure 6. Timeseries of the self-excited mechanical system. Modal energy contents E (solid) and E 2 (dotted), total energy content E tot = E +E 2, impulsive strength scaling factor ε k (left), and physical displacements x and x 2 (right) for τ = τ p. Grey-colored lines denote results of the corresponding system without impulsive excitation. Initial condition: initial velocity of mass #2. Figure 7. Stability chart for variation of the system parameter M and the constant timespan τ between impulses. Grey=unstable, white=asymptotically stable trivial solution. Up to now, the stability properties for a constant set of system parameters was studied. Figure 7 displays the results of a stability investigation for different values of the mass M and the
12 MOVIC26 & RASD26 Journal of Physics: Conference Series 744 (26) 2 doi:.88/ /744//2 timespan τ between impulses. For all values of M within the interval [.5,2], the system without impulsive force excitation is unstable. Gray-colored areas in Fig. 7 denote instability, whereas white-colored ones represent an asymptotically stable trivial solution. The stability threshold max λ i = is marked by the solid black lines. The previously investigated set of parameters M = and τ = τ p is indicated by the dashed-dotted lines, and is part of a narrow asymptotically stable area which becomes wider with increasing M and shifts to higher values of τ. Two large areas of stability are observed in the vicinity of τ 4.9 and M.6. Moreover, additional areas of stability appear near τ 9.5 and τ 4.4, which look similar to the foregoing. Figure 7 also demonstrates that the proposed impulsive forcing allows to suppress self-excited vibrations for almost all values of M within the interval [.5,2] by choosing a proper value of τ. 4. Conclusions A new method of suppressing self-excited vibrations of mechanical systems by introducing impulsive forcing was presented in this contribution. It was shown that a state-dependent impulsive strength exists, which allows to shift discrete amounts of energy from one mode of vibration to the other. In this special case, no energy is added to the mechanical system by the impulsive forces. The stability properties of the mechanical system can be investigated easily by calculating eigenvalues of a set of difference equations. It was demonstrated, that this method is capable to suppress self-excited vibrations of mechanical systems. Acknowledgments This work has been supported by the Austrian COMET-K2 programme of the Linz Center of Mechatronics (LCM), and has been funded by the Austrian federal government and the federal state of Upper Austria. References [] Gendelman O V 2 Targeted energy transfer in systems with external and self-excitation Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225(9) pp [2] Vakakis A F, Gendelman O V, Bergman L A, McFarland D M, Kerschen G, Lee Y S 29 Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems (Springer Netherlands) [3] Al-Shudeifat M A, Vakakis A F, Bergman L A 25 Shock mitigation by means of low to high-frequency nonlinear targeted energy transfers in a large-scale structure ASME Journal of Computational and Nonlinear Dynamics (2) [4] Dohnal F 28 Damping by parametric stiffness excitation: Resonance and anti-resonance Journal of Vibration and Control 4(5) pp [5] Ecker H, Pumhössel T 22 Vibration suppression and energy transfer by parametric excitation in drive systems. Proc. IMechE Part C: J. Mechanical Engineering Science 226(8), pp 2-24 [6] Tondl A 998 To the problem of quenching self-excited vibrations Acta Technicae CSAV 43 pp 9-6 [7] Diaz A R, Mukherjee R, Cai T 23 Vibration control of tension-aligned structures Proc. of the th Int. Conf. on Vibration Problems (ICOVP), Lisbon, Portugal [8] Pumhössel T, Hehenberger P, Zeman K 23 On the effect of impulsive parametric excitation to the modal energy content of Hamiltonian systems Proc. of the th Int. Conf. on Vibration Problems (ICOVP), Lisbon, Portugal [9] Pumhössel T 25 A contribution to the reduction of self-excited vibrations of dynamical systems by impulsive parametric excitation Proc. of the Int. Conf. on Engineering Vibration (ICoEV), Ljubljana, Slovenia [] Angeles J 22 Dynamic Response of Linear Mechanical Systems (Springer US) [] Hsu C S 972 Impulsive Parametric Excitation: Theory Journal of Applied Mechanics 39(2) pp [2] Elaydi S 25 An Introduction to Difference Equations 3rd ed (New York: Springer-Verlag)
Integration of a nonlinear energy sink and a piezoelectric energy harvester
Appl. Math. Mech. -Engl. Ed., 38(7), 1019 1030 (2017) DOI 10.1007/s10483-017-2220-6 c Shanghai University and Springer-Verlag Berlin Heidelberg 2017 Applied Mathematics and Mechanics (English Edition)
More informationJournal of Sound and Vibration
Journal of Sound and Vibration 330 (2011) 1 8 Contents lists available at ScienceDirect Journal of Sound and Vibration journal homepage: www.elsevier.com/locate/jsvi Rapid Communications Enhanced passive
More informationLimit cycle oscillations at resonances
IOP Conference Series: Materials Science and Engineering PAPER OPEN ACCESS Limit cycle oscillations at resonances To cite this article: K Hellevik and O T Gudmestad 2017 IOP Conf. Ser.: Mater. Sci. Eng.
More informationReliability-based Design Optimization of Nonlinear Energy Sinks
th World Congress on Structural and Multidisciplinary Optimization 7 th - th, June, Sydney Australia Reliability-based Design Optimization of Nonlinear Energy Sinks Ethan Boroson and Samy Missoum University
More information1. Multiple Degree-of-Freedom (MDOF) Systems: Introduction
1. Multiple Degree-of-Freedom (MDOF) Systems: Introduction Lesson Objectives: 1) List examples of MDOF structural systems and state assumptions of the idealizations. 2) Formulate the equation of motion
More informationStudy on Tire-attached Energy Harvester for Lowspeed Actual Vehicle Driving
Journal of Physics: Conference Series PAPER OPEN ACCESS Study on Tire-attached Energy Harvester for Lowspeed Actual Vehicle Driving To cite this article: Y Zhang et al 15 J. Phys.: Conf. Ser. 66 116 Recent
More informationApplication of the Shannon-Kotelnik theorem on the vortex structures identification
IOP Conference Series: Earth and Environmental Science OPEN ACCESS Application of the Shannon-Kotelnik theorem on the vortex structures identification To cite this article: F Pochylý et al 2014 IOP Conf.
More informationChapter 23: Principles of Passive Vibration Control: Design of absorber
Chapter 23: Principles of Passive Vibration Control: Design of absorber INTRODUCTION The term 'vibration absorber' is used for passive devices attached to the vibrating structure. Such devices are made
More informationNonlinear dynamics of structures with propagating cracks
Loughborough University Institutional Repository Nonlinear dynamics of structures with propagating cracks This item was submitted to Loughborough University's Institutional Repository by the/an author.
More informationSIMULATION AND TESTING OF A 6-STORY STRUCTURE INCORPORATING A COUPLED TWO MASS NONLINEAR ENERGY SINK. Sean Hubbard Dept. of Aerospace Engineering
Proceedings of the ASME 1 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 1 August 1-15, 1, Chicago, IL, USA DETC1-7144 SIMULATION
More informationIdentification Methods for Structural Systems. Prof. Dr. Eleni Chatzi Lecture March, 2016
Prof. Dr. Eleni Chatzi Lecture 4-09. March, 2016 Fundamentals Overview Multiple DOF Systems State-space Formulation Eigenvalue Analysis The Mode Superposition Method The effect of Damping on Structural
More informationEQUIVALENT SINGLE-DEGREE-OF-FREEDOM SYSTEM AND FREE VIBRATION
1 EQUIVALENT SINGLE-DEGREE-OF-FREEDOM SYSTEM AND FREE VIBRATION The course on Mechanical Vibration is an important part of the Mechanical Engineering undergraduate curriculum. It is necessary for the development
More informationLECTURE 14: DEVELOPING THE EQUATIONS OF MOTION FOR TWO-MASS VIBRATION EXAMPLES
LECTURE 14: DEVELOPING THE EQUATIONS OF MOTION FOR TWO-MASS VIBRATION EXAMPLES Figure 3.47 a. Two-mass, linear vibration system with spring connections. b. Free-body diagrams. c. Alternative free-body
More informationComputational Simulation of Dynamic Response of Vehicle Tatra T815 and the Ground
IOP Conference Series: Earth and Environmental Science PAPER OPEN ACCESS Computational Simulation of Dynamic Response of Vehicle Tatra T815 and the Ground To cite this article: Jozef Vlek and Veronika
More informationLab #2 - Two Degrees-of-Freedom Oscillator
Lab #2 - Two Degrees-of-Freedom Oscillator Last Updated: March 0, 2007 INTRODUCTION The system illustrated in Figure has two degrees-of-freedom. This means that two is the minimum number of coordinates
More information3 Mathematical modeling of the torsional dynamics of a drill string
3 Mathematical modeling of the torsional dynamics of a drill string 3.1 Introduction Many works about torsional vibrations on drilling systems [1, 12, 18, 24, 41] have been published using different numerical
More informationParametric Excitation of a Linear Oscillator
Parametric Excitation of a Linear Oscillator Manual Eugene Butikov Annotation. The manual includes a description of the simulated physical system and a summary of the relevant theoretical material for
More informationRESPONSE OF NON-LINEAR SHOCK ABSORBERS-BOUNDARY VALUE PROBLEM ANALYSIS
Int. J. of Applied Mechanics and Engineering, 01, vol.18, No., pp.79-814 DOI: 10.478/ijame-01-0048 RESPONSE OF NON-LINEAR SHOCK ABSORBERS-BOUNDARY VALUE PROBLEM ANALYSIS M.A. RAHMAN *, U. AHMED and M.S.
More informationStability and bifurcation analysis of a Van der Pol Duffing oscillator with a nonlinear tuned vibration absorber
ENO 4, July 6-, 4, Vienna, Austria Stability and bifurcation analysis of a Van der Pol Duffing oscillator with a nonlinear tuned vibration absorber Giuseppe Habib and Gaetan Kerschen Department of Aerospace
More informationNatural frequency analysis of fluid-conveying pipes in the ADINA system
Journal of Physics: Conference Series OPEN ACCESS Natural frequency analysis of fluid-conveying pipes in the ADINA system To cite this article: L Wang et al 2013 J. Phys.: Conf. Ser. 448 012014 View the
More informationDamping Performance of Taut Cables with Passive Absorbers Incorporating Inerters
Journal of Physics: Conference Series PAPER OPEN ACCESS Damping Performance of Taut Cables with Passive Absorbers Incorporating Inerters To cite this article: Jiannan Luo et al 2016 J. Phys.: Conf. Ser.
More informationNON-STATIONARY RESONANCE DYNAMICS OF THE HARMONICALLY FORCED PENDULUM
CYBERNETICS AND PHYSICS, VOL. 5, NO. 3, 016, 91 95 NON-STATIONARY RESONANCE DYNAMICS OF THE HARMONICALLY FORCED PENDULUM Leonid I. Manevitch Polymer and Composite Materials Department N. N. Semenov Institute
More informationBifurcation control and chaos in a linear impulsive system
Vol 8 No 2, December 2009 c 2009 Chin. Phys. Soc. 674-056/2009/82)/5235-07 Chinese Physics B and IOP Publishing Ltd Bifurcation control and chaos in a linear impulsive system Jiang Gui-Rong 蒋贵荣 ) a)b),
More informationQuantum phase transition and conductivity of parallel quantum dots with a moderate Coulomb interaction
Journal of Physics: Conference Series PAPER OPEN ACCESS Quantum phase transition and conductivity of parallel quantum dots with a moderate Coulomb interaction To cite this article: V S Protsenko and A
More informationAdvanced Vibrations. Elements of Analytical Dynamics. By: H. Ahmadian Lecture One
Advanced Vibrations Lecture One Elements of Analytical Dynamics By: H. Ahmadian ahmadian@iust.ac.ir Elements of Analytical Dynamics Newton's laws were formulated for a single particle Can be extended to
More informationThe Stick-Slip Vibration and Bifurcation of a Vibro-Impact System with Dry Friction
Send Orders for Reprints to reprints@benthamscience.ae 308 The Open Mechanical Engineering Journal, 2014, 8, 308-313 Open Access The Stick-Slip Vibration and Bifurcation of a Vibro-Impact System with Dry
More informationEffect of an hourglass shaped sleeve on the performance of the fluid dynamic bearings of a HDD spindle motor
DOI 10.1007/s00542-014-2136-5 Technical Paper Effect of an hourglass shaped sleeve on the performance of the fluid dynamic bearings of a HDD spindle motor Jihoon Lee Minho Lee Gunhee Jang Received: 14
More informationarxiv: v1 [nlin.ao] 15 Jan 2019
The tuned bistable nonlinear energy sink Giuseppe Habib 1, Francesco Romeo arxiv:191.5435v1 [nlin.ao] 15 Jan 19 1 Department of Aerospace and Mechanical Engineering, University of Liege, Liege, Belgium.
More informationDesign of Structures for Earthquake Resistance
NATIONAL TECHNICAL UNIVERSITY OF ATHENS Design of Structures for Earthquake Resistance Basic principles Ioannis N. Psycharis Lecture 3 MDOF systems Equation of motion M u + C u + K u = M r x g(t) where:
More informationClearly the passage of an eigenvalue through to the positive real half plane leads to a qualitative change in the phase portrait, i.e.
Bifurcations We have already seen how the loss of stiffness in a linear oscillator leads to instability. In a practical situation the stiffness may not degrade in a linear fashion, and instability may
More informationInvestigation on fluid added mass effect in the modal response of a pump-turbine runner
IOP Conference Series: Materials Science and Engineering OPEN ACCESS Investigation on fluid added mass effect in the modal response of a pump-turbine runner To cite this article: L Y He et al 2013 IOP
More informationResearch Article Dynamics of an Autoparametric Pendulum-Like System with a Nonlinear Semiactive Suspension
Mathematical Problems in Engineering Volume, Article ID 57, 5 pages doi:.55//57 Research Article Dynamics of an Autoparametric Pendulum-Like System with a Nonlinear Semiactive Suspension Krzysztof Kecik
More informationCoherence of Noisy Oscillators with Delayed Feedback Inducing Multistability
Journal of Physics: Conference Series PAPER OPEN ACCESS Coherence of Noisy Oscillators with Delayed Feedback Inducing Multistability To cite this article: Anastasiya V Pimenova and Denis S Goldobin 2016
More informationSync or anti-sync dynamical pattern selection in coupled self-sustained oscillator systems
Journal of Physics: Conference Series OPEN ACCESS Sync or anti-sync dynamical pattern selection in coupled self-sustained oscillator systems To cite this article: Larissa Davidova et al 2014 J. Phys.:
More informationTheory of Vibrations in Stewart Platforms
Theory of Vibrations in Stewart Platforms J.M. Selig and X. Ding School of Computing, Info. Sys. & Maths. South Bank University London SE1 0AA, U.K. (seligjm@sbu.ac.uk) Abstract This article develops a
More informationCOMPOSITE MATERIAL WITH NEGATIVE STIFFNESS INCLUSION FOR VIBRATION DAMPING: THE EFFECT OF A NONLINEAR BISTABLE ELEMENT
11 th International Conference on Vibration Problems Z. Dimitrovová et.al. (eds.) Lisbon, Portugal, 9 12 September 2013 COMPOSITE MATERIAL WITH NEGATIVE STIFFNESS INCLUSION FOR VIBRATION DAMPING: THE EFFECT
More informationAnalysis of Tensioner Induced Coupling in Serpentine Belt Drive Systems
2008-01-1371 of Tensioner Induced Coupling in Serpentine Belt Drive Systems Copyright 2007 SAE International R. P. Neward and S. Boedo Department of Mechanical Engineering, Rochester Institute of Technology
More informationAutoparametric Resonance in Mechanical Systems. Thijs Ruijgrok Ferdinand Verhulst Radoslav Nabergoj
Autoparametric Resonance in Mechanical Systems Aleš Tondl Thijs Ruijgrok Ferdinand Verhulst Radoslav Nabergoj PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE The Pitt Building, Trumpington
More informationAA242B: MECHANICAL VIBRATIONS
AA242B: MECHANICAL VIBRATIONS 1 / 50 AA242B: MECHANICAL VIBRATIONS Undamped Vibrations of n-dof Systems These slides are based on the recommended textbook: M. Géradin and D. Rixen, Mechanical Vibrations:
More informationStability Analysis of a Hydrodynamic Journal Bearing With Rotating Herringbone Grooves
G. H. Jang e-mail: ghjang@hanyang.ac.kr J. W. Yoon PREM, Department of Mechanical Engineering, Hanyang University, Seoul, 33-79, Korea Stability Analysis of a Hydrodynamic Journal Bearing With Rotating
More informationTheoretical Basis of Modal Analysis
American Journal of Mechanical Engineering, 03, Vol., No. 7, 73-79 Available online at http://pubs.sciepub.com/ajme//7/4 Science and Education Publishing DOI:0.69/ajme--7-4 heoretical Basis of Modal Analysis
More informationA NEW METHOD FOR VIBRATION MODE ANALYSIS
Proceedings of IDETC/CIE 25 25 ASME 25 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference Long Beach, California, USA, September 24-28, 25 DETC25-85138
More informationRobust shaft design to compensate deformation in the hub press fitting and disk clamping process of 2.5 HDDs
DOI 10.1007/s00542-016-2850-2 TECHNICAL PAPER Robust shaft design to compensate deformation in the hub press fitting and disk clamping process of 2.5 HDDs Bumcho Kim 1,2 Minho Lee 3 Gunhee Jang 3 Received:
More informationDynamics of Structures
Dynamics of Structures Elements of structural dynamics Roberto Tomasi 11.05.2017 Roberto Tomasi Dynamics of Structures 11.05.2017 1 / 22 Overview 1 SDOF system SDOF system Equation of motion Response spectrum
More informationEarthquake Excited Base-Isolated Structures Protected by Tuned Liquid Column Dampers: Design Approach and Experimental Verification
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 199 017 1574 1579 X International Conference on Structural Dynamics, EURODYN 017 Earthquake Excited Base-Isolated Structures
More informationModal Decomposition and the Time-Domain Response of Linear Systems 1
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING.151 Advanced System Dynamics and Control Modal Decomposition and the Time-Domain Response of Linear Systems 1 In a previous handout
More informationPrediction of high-frequency responses in the time domain by a transient scaling approach
Prediction of high-frequency responses in the time domain by a transient scaling approach X.. Li 1 1 Beijing Municipal Institute of Labor Protection, Beijing Key Laboratory of Environmental Noise and Vibration,
More informationNONLINEAR NORMAL MODES OF COUPLED SELF-EXCITED OSCILLATORS
NONLINEAR NORMAL MODES OF COUPLED SELF-EXCITED OSCILLATORS Jerzy Warminski 1 1 Department of Applied Mechanics, Lublin University of Technology, Lublin, Poland, j.warminski@pollub.pl Abstract: The main
More informationForce, displacement and strain nonlinear transfer function estimation.
Journal of Physics: Conference Series PAPER OPEN ACCESS Force, displacement and strain nonlinear transfer function estimation. To cite this article: K A Sweitzer and N S Ferguson 2016 J. Phys.: Conf. Ser.
More informationDifference Resonances in a controlled van der Pol-Duffing oscillator involving time. delay
Difference Resonances in a controlled van der Pol-Duffing oscillator involving time delay This paper was published in the journal Chaos, Solitions & Fractals, vol.4, no., pp.975-98, Oct 9 J.C. Ji, N. Zhang,
More informationThe Effect of a Rotational Spring on the Global Stability Aspects of the Classical von Mises Model under Step Loading
Copyright cfl 2001 Tech Science Press CMES, vol.2, no.1, pp.15-26, 2001 The Effect of a Rotational Spring on the Global Stability Aspects of the Classical von Mises Model under Step Loading D. S. Sophianopoulos
More informationDynamics of a mass-spring-pendulum system with vastly different frequencies
Dynamics of a mass-spring-pendulum system with vastly different frequencies Hiba Sheheitli, hs497@cornell.edu Richard H. Rand, rhr2@cornell.edu Cornell University, Ithaca, NY, USA Abstract. We investigate
More informationEXPLORING TARGETED ENERGY TRANSFER FOR VIBRATION DAMPING IN NONLINEAR PIEZOELECTRIC SHUNTS
Exploring Targeted Energy Transfer for Vibration Damping in Nonlinear Piezoelectric Shunts VIII ECCOMAS Thematic Conference on Smart Structures and Materials SMART 217 A. Güemes, A. Beneddou, J. Rodellar
More informationCE 6701 Structural Dynamics and Earthquake Engineering Dr. P. Venkateswara Rao
CE 6701 Structural Dynamics and Earthquake Engineering Dr. P. Venkateswara Rao Associate Professor Dept. of Civil Engineering SVCE, Sriperumbudur Difference between static loading and dynamic loading Degree
More informationDamping of materials and members in structures
Journal of Physics: Conference Series Damping of materials and members in structures To cite this article: F Orban 0 J. Phys.: Conf. Ser. 68 00 View the article online for updates and enhancements. Related
More informationModal Analysis: What it is and is not Gerrit Visser
Modal Analysis: What it is and is not Gerrit Visser What is a Modal Analysis? What answers do we get out of it? How is it useful? What does it not tell us? In this article, we ll discuss where a modal
More informationNonlinear Stability and Bifurcation of Multi-D.O.F. Chatter System in Grinding Process
Key Engineering Materials Vols. -5 (6) pp. -5 online at http://www.scientific.net (6) Trans Tech Publications Switzerland Online available since 6//5 Nonlinear Stability and Bifurcation of Multi-D.O.F.
More informationFuzzy modeling and control of rotary inverted pendulum system using LQR technique
IOP Conference Series: Materials Science and Engineering OPEN ACCESS Fuzzy modeling and control of rotary inverted pendulum system using LQR technique To cite this article: M A Fairus et al 13 IOP Conf.
More informationImplementation of an advanced beam model in BHawC
Journal of Physics: Conference Series PAPER OPEN ACCESS Implementation of an advanced beam model in BHawC To cite this article: P J Couturier and P F Skjoldan 28 J. Phys.: Conf. Ser. 37 625 Related content
More informationElectromagnetic modulation of monochromatic neutrino beams
Journal of Physics: Conference Series PAPER OPEN ACCESS Electromagnetic modulation of monochromatic neutrino beams To cite this article: A L Barabanov and O A Titov 2016 J. Phys.: Conf. Ser. 675 012009
More informationUniversity of Bristol - Explore Bristol Research. Publisher's PDF, also known as Version of record
Noel, J. P., Renson, L., & Kerschen, G. (214). Experimental analysis of 2:1 modal interactions with noncommensurate linear frequencies in an aerospace structure. In ENOC 214 - Proceedings of 8th European
More informationDESIGN OF A NONLINEAR VIBRATION ABSORBER
DESIGN OF A NONLINEAR VIBRATION ABSORBER Maxime Geeroms, Laurens Marijns, Mia Loccufier and Dirk Aeyels Ghent University, Department EESA, Belgium Abstract Linear vibration absorbers can only capture certain
More informationPassive Control of the Vibration of Flooring Systems using a Gravity Compensated Non-Linear Energy Sink
The 3 th International Workshop on Advanced Smart Materials and Smart Structures Technology July -3, 7, The University of Tokyo, Japan Passive Control of the Vibration of Flooring Systems using a Gravity
More informationExperimental demonstration of a 3D-printed nonlinear tuned vibration absorber
Experimental demonstration of a 3D-printed nonlinear tuned vibration absorber C. Grappasonni, G. Habib, T. Detroux G. Kerschen Space Structures and Systems Laboratory (S3L) Department of Aerospace and
More informationα Cubic nonlinearity coefficient. ISSN: x DOI: : /JOEMS
Journal of the Egyptian Mathematical Society Volume (6) - Issue (1) - 018 ISSN: 1110-65x DOI: : 10.1608/JOEMS.018.9468 ENHANCING PD-CONTROLLER EFFICIENCY VIA TIME- DELAYS TO SUPPRESS NONLINEAR SYSTEM OSCILLATIONS
More informationMath 216 Final Exam 24 April, 2017
Math 216 Final Exam 24 April, 2017 This sample exam is provided to serve as one component of your studying for this exam in this course. Please note that it is not guaranteed to cover the material that
More informationDYNAMICS OF ESSENTIALLY NONLINEAR VIBRATION ABSORBER COUPLED TO HARMONICALLY EXCITED 2 DOF SYSTEM
ENOC 008, Saint Petersburg, Russia, June, 0-July, 4 008 DYNAMICS OF ESSENTIALLY NONLINEAR VIBRATION ABSORBER COUPLED TO HARMONICALLY EXCITED DOF SYSTEM Yuli Starosetsky Faculty of Mechanical Engineering
More informationImproving convergence of incremental harmonic balance method using homotopy analysis method
Acta Mech Sin (2009) 25:707 712 DOI 10.1007/s10409-009-0256-4 RESEARCH PAPER Improving convergence of incremental harmonic balance method using homotopy analysis method Yanmao Chen Jike Liu Received: 10
More informationSuppression of the primary resonance vibrations of a forced nonlinear system using a dynamic vibration absorber
Suppression of the primary resonance vibrations of a forced nonlinear system using a dynamic vibration absorber J.C. Ji, N. Zhang Faculty of Engineering, University of Technology, Sydney PO Box, Broadway,
More informationPassive non-linear targeted energy transfer and its applications to vibration absorption: a review
INVITED REVIEW 77 Passive non-linear targeted energy transfer and its applications to vibration absorption: a review Y S Lee 1, A F Vakakis 2, L A Bergman 1, D M McFarland 1, G Kerschen 3, F Nucera 4,
More informationStability of transverse vibration of rod under longitudinal step-wise loading
Journal of Physics: Conference Series OPEN ACCESS Stability of transverse vibration of rod under longitudinal step-wise loading To cite this article: A K Belyaev et al 013 J. Phys.: Conf. Ser. 51 0103
More informationA study on calculation method for mechanical impedance of air spring
Journal of Physics: Conference Series PAPER OPEN ACCESS A study on calculation method for mechanical impedance of air spring To cite this article: SHAI Changgeng et al 6 J. Phys.: Conf. Ser. 744 8 View
More informationQuasi-particle current in planar Majorana nanowires
Journal of Physics: Conference Series PAPER OPEN ACCESS Quasi-particle current in planar Majorana nanowires To cite this article: Javier Osca and Llorenç Serra 2015 J. Phys.: Conf. Ser. 647 012063 Related
More informationDetermining the Critical Point of a Sigmoidal Curve via its Fourier Transform
Journal of Physics: Conference Series PAPER OPEN ACCESS Determining the Critical Point of a Sigmoidal Curve via its Fourier Transform To cite this article: Ayse Humeyra Bilge and Yunus Ozdemir 6 J. Phys.:
More informatione jωt = cos(ωt) + jsin(ωt),
This chapter introduces you to the most useful mechanical oscillator model, a mass-spring system with a single degree of freedom. Basic understanding of this system is the gateway to the understanding
More informationOpen Access Semi-active Pneumatic Devices for Control of MDOF Structures
The Open Construction and Building Technology Journal, 2009, 3, 141-145 141 Open Access Semi-active Pneumatic Devices for Control of MDOF Structures Y. Ribakov* Department of Civil Engineering, Ariel University
More informationDetermination of Dynamic Characteristics of the Frame Bearing Structures of the Vibrating Separating Machines
IOP Conference Series: Materials Science and Engineering PAPER OPEN ACCESS Determination of Dynamic Characteristics of the Frame Bearing Structures of the Vibrating Separating Machines To cite this article:
More informationResearch Article The Microphone Feedback Analogy for Chatter in Machining
Shock and Vibration Volume 215, Article ID 976819, 5 pages http://dx.doi.org/1.1155/215/976819 Research Article The Microphone Feedback Analogy for Chatter in Machining Tony Schmitz UniversityofNorthCarolinaatCharlotte,Charlotte,NC28223,USA
More information1 Introduction. Minho Lee 1 Jihoon Lee 1 Gunhee Jang 1
DOI 10.1007/s005-015-5-5 TECHNICAL PAPER Stability analysis of a whirling rigid rotor supported by stationary grooved FDBs considering the five degrees of freedom of a general rotor bearing system Minho
More informationSome Aspects of Structural Dynamics
Appendix B Some Aspects of Structural Dynamics This Appendix deals with some aspects of the dynamic behavior of SDOF and MDOF. It starts with the formulation of the equation of motion of SDOF systems.
More informationLeast action principle and stochastic motion : a generic derivation of path probability
Journal of Physics: Conference Series PAPER OPEN ACCESS Least action principle and stochastic motion : a generic derivation of path probability To cite this article: Aziz El Kaabouchi and Qiuping A Wang
More informationMODal ENergy Analysis
MODal ENergy Analysis Nicolas Totaro, Jean-Louis Guyader To cite this version: Nicolas Totaro, Jean-Louis Guyader. MODal ENergy Analysis. RASD, Jul 2013, Pise, Italy. 2013. HAL Id: hal-00841467
More informationVibration analysis of concrete bridges during a train pass-by using various models
Journal of Physics: Conference Series PAPER OPEN ACCESS Vibration analysis of concrete bridges during a train pass-by using various models To cite this article: Qi Li et al 2016 J. Phys.: Conf. Ser. 744
More informationOptimal joint placement and modal disparity in control of flexible structures
Computers and Structures xxx (2007) xxx xxx www.elsevier.com/locate/compstruc Optimal joint placement and modal disparity in control of flexible structures Alejandro R. Diaz *, Ranjan Mukherjee Mechanical
More informationCorrelation spectroscopy
1 TWO-DIMENSIONAL SPECTROSCOPY Correlation spectroscopy What is two-dimensional spectroscopy? This is a method that will describe the underlying correlations between two spectral features. Our examination
More informationTransient response prediction of an impulsively excited structure using a scaling approach
Numerical Techniques (others): Paper ICA2016-668 Transient response prediction of an impulsively excited structure using a scaling approach Xianhui Li (a), Jing Zhang (b), Tuo Xing (c) (a) Beijing Municipal
More informationAdditive resonances of a controlled van der Pol-Duffing oscillator
Additive resonances of a controlled van der Pol-Duffing oscillator This paper has been published in Journal of Sound and Vibration vol. 5 issue - 8 pp.-. J.C. Ji N. Zhang Faculty of Engineering University
More informationThe Behaviour of Simple Non-Linear Tuned Mass Dampers
ctbuh.org/papers Title: Authors: Subject: Keyword: The Behaviour of Simple Non-Linear Tuned Mass Dampers Barry J. Vickery, University of Western Ontario Jon K. Galsworthy, RWDI Rafik Gerges, HSA & Associates
More informationLaboratory handout 5 Mode shapes and resonance
laboratory handouts, me 34 82 Laboratory handout 5 Mode shapes and resonance In this handout, material and assignments marked as optional can be skipped when preparing for the lab, but may provide a useful
More informationDAMPING MODELLING AND IDENTIFICATION USING GENERALIZED PROPORTIONAL DAMPING
DAMPING MODELLING AND IDENTIFICATION USING GENERALIZED PROPORTIONAL DAMPING S. Adhikari Department of Aerospace Engineering, University of Bristol, Queens Building, University Walk, Bristol BS8 1TR (U.K.)
More informationWavelet analysis of the parameters of edge plasma fluctuations in the L-2M stellarator
Journal of Physics: Conference Series PAPER OPEN ACCESS Wavelet analysis of the parameters of edge plasma fluctuations in the L-2M stellarator To cite this article: S A Maslov et al 2016 J. Phys.: Conf.
More informationChaotic motion. Phys 750 Lecture 9
Chaotic motion Phys 750 Lecture 9 Finite-difference equations Finite difference equation approximates a differential equation as an iterative map (x n+1,v n+1 )=M[(x n,v n )] Evolution from time t =0to
More informationOn optimal performance of nonlinear energy sinks in multiple-degree-of-freedom systems
MITSUBISHI ELECTRIC RESEARCH LABORATORIES http://www.merl.com On optimal performance of nonlinear energy sinks in multiple-degree-of-freedom systems Tripathi, A.; Grover, P.; Kalmar-Nagy, T. TR2017-003
More informationElectron detachment process in collisions of negative hydrogen ions with hydrogen molecules
Journal of Physics: Conference Series PAPER OPEN ACCESS Electron detachment process in collisions of negative hydrogen ions with hydrogen molecules To cite this article: O V Aleksandrovich et al 1 J. Phys.:
More informationDynamical behaviour of a controlled vibro-impact system
Vol 17 No 7, July 2008 c 2008 Chin. Phys. Soc. 1674-1056/2008/17(07)/2446-05 Chinese Physics B and IOP Publishing Ltd Dynamical behaviour of a controlled vibro-impact system Wang Liang( ), Xu Wei( ), and
More informationStochastic Dynamics of SDOF Systems (cont.).
Outline of Stochastic Dynamics of SDOF Systems (cont.). Weakly Stationary Response Processes. Equivalent White Noise Approximations. Gaussian Response Processes as Conditional Normal Distributions. Stochastic
More informationAA 242B / ME 242B: Mechanical Vibrations (Spring 2016)
AA 242B / ME 242B: Mechanical Vibrations (Spring 206) Solution of Homework #3 Control Tab Figure : Schematic for the control tab. Inadequacy of a static-test A static-test for measuring θ would ideally
More informationME 563 HOMEWORK # 5 SOLUTIONS Fall 2010
ME 563 HOMEWORK # 5 SOLUTIONS Fall 2010 PROBLEM 1: You are given the lumped parameter dynamic differential equations of motion for a two degree-offreedom model of an automobile suspension system for small
More informationThe Modeling of Single-dof Mechanical Systems
The Modeling of Single-dof Mechanical Systems Lagrange equation for a single-dof system: where: q: is the generalized coordinate; T: is the total kinetic energy of the system; V: is the total potential
More information1792. On the conditions for synchronous harmonic free vibrations
1792. On the conditions for synchronous harmonic free vibrations César A. Morales Departamento de Mecánica, Universidad Simón Bolívar, Apdo. 89000, Caracas 1080A, Venezuela E-mail: cmorales@usb.ve (Received
More information